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Explain small signal model of PN junction diode
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• In a small signal model, we can take a nonlinear circuit or device and make approximations which linearize it about an DC operating point.

• To do this, we write all voltages and currents as the sum of a DC value for each, plus a small extra amount which is the small signal.

• Consider the above circuit,

Input voltage is vD(t)=VD+vd(t)

enter image description here

• DC analysis: The purpose of DC analysis is to find the operating point of diode. To do DC analysis, turn off the small AC signal

The voltage vD(t)=VDvD(t)=VD

And the current iD(t)=ID=ISexp(VDηvT)

enter image description here

• When small AC signal is applied

Total Voltage across diode is vD(t)=VD+vd(t)vD(t)=VD+vd(t)

Total instantaneous current is iD(t)=ISexp(VD+vd(t)ηvT)iD(t)=ISexp(VD+vd(t)ηvT)

iD(t)=ISexp(VDηvT)×exp(vd(t)ηvT)iD(t)=ISexp(VDηvT)×exp(vd(t)ηvT)

iD(t)=ID×exp(vd(t)ηvT)iD(t)=ID×exp(vd(t)ηvT)

When vd(t)<<ηvTvd(t)<<ηvT hence (vd(t)ηvT<<1)(vd(t)ηvT<<1) therefore we can ignore powers of vd(t)ηvTvd(t)ηvT

expvd(t)ηvT)1+vd(t)ηvTexpvd(t)ηvT)1+vd(t)ηvT

iD(t)ID(1+vd(t)ηvT)iD(t)ID(1+vd(t)ηvT)

iD(t)ID+IDηvTvd(t)iD(t)ID+IDηvTvd(t)

iD(t)=ID+id(t)iD(t)=ID+id(t)

id(t)=IDηvTvd(t)id(t)=IDηvTvd(t)

Since IDηvT is a ratio of current and voltage hence we can replace it by resistance

Inverse of IDηvT=ηvTID=rdIDηvT=ηvTID=rd

• Small signal AC equivalent circuit is

enter image description here

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